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arXiv:1905.02193

Universality of Diffractive Collisions and the Quantum Pressure Standard

James L. Booth, Pinrui Shen, Roman V. Krems, Kirk W. Madison

Published May 3, 2019• 0 citations
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Abstract

This work demonstrates that quantum diffractive collisions, those that result in very small momentum and energy transfer, are universal. Specifically, the cumulative energy distribution transferred to an initially stationary sensor particle by a quantum diffractive collision follows a universal function that depends only on the sensor particle mass and the thermally-averaged, total collision cross section. The characteristic energy scale corresponds to the localization length associated with the collision-induced quantum measurement, and the shape of the universal function is determined {\it only} by the analytic form of the interaction potential at long range. Using cold $^{87}$Rb sensor atoms confined in a magnetic trap, we observe experimentally the universal function specific to van der Waals collisions, and realize a \emph{self-defining} particle pressure sensor that can be used for any ambient gas. This provides the first primary and quantum definition of the Pascal, applicable to any species and therefore represents a key advance for vacuum and pressure metrology. The quantum pressure standard realized here was compared with a state-of-the-art orifice flow standard transferred by an ionization gauge calibrated for N$_2$. The pressure measurements agreed at the 0.5\% level.

DOI
10.48550/arxiv.1905.02193

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This work demonstrates that quantum diffractive collisions, those that result in very small momentum and energy transfer, are universal. Specifically, the cumulative energy distribution transferred to an initially stationary sensor particle by a quantum diffractive collision follows a universal function that depends only on the sensor particle mass and the thermally-averaged, total collision cross section. The characteristic energy scale corresponds to the localization length associated with the collision-induced quantum measurement, and the shape of the universal function is determined {\it only} by the analytic form of the interaction potential at long range. Using cold 87^{87}87Rb sensor atoms confined in a magnetic trap, we observe experimentally the universal function specific to van der Waals collisions, and realize a \emph{self-defining} particle pressure sensor that can be used for any ambient gas. This provides the first primary and quantum definition of the Pascal, applicable to any species and therefore represents a key advance for vacuum and pressure metrology. The quantum pressure standard realized here was compared with a state-of-the-art orifice flow standard transferred by an ionization gauge calibrated for N2_22​. The pressure measurements agreed at the 0.5% level.
Abstract This work demonstrates that quantum diffractive collisions are governed by a universal law characterized by a single parameter that can be determined experimentally. Specifically, we report a quantitative form of the universal, cumulative energy distribution transferred to initially stationary sensor particles by quantum diffractive collisions. The characteristic energy scale corresponds to the localization length associated with the collision-induced quantum measurement, and the shape of the universal function is determined only by the analytic form of the interaction potential at long range. Using cold 87Rb sensor atoms confined in a magnetic trap, we observe experimentally p QDU 6 , the universal function specific to van der Waals collisions, and use it to realize a self-defining particle pressure sensor that can be used for any ambient gas. This provides the first primary and quantum definition of the Pascal, applicable to any species and therefore represents a fundamental advance for vacuum and pressure metrology. The quantum pressure standard realized here is compared with a state-of-the-art orifice flow standard transferred by an ionization gauge calibrated for N2. The pressure measurements agree at the 0.5% level.
Abstract We report the realization of the first cold-atom primary standard. This standard is based on a universal law governing quantum diffractive collisions between particles that allows an experimental determination of the velocity averaged total collision cross section, the only parameter required to quantify the pressure or flux of particles given a sensor particle collision rate measurement. Using an ensemble of 87Rb sensor atoms, we show that this new quantum pressure standard can be applied to gases of both atomic (He, Ar, and Xe) and molecular species ( N 2 , C O 2 , and H 2 ), surpassing the scope of existing orifice flow pressure standards. We verify the accuracy of this new standard using an ionization gauge (IG) calibrated for N2 by an orifice flow standard. The gauge calibration factors determined by the cold atom and orifice flow standards differ by less than 0.5% and, thus, agree within their uncertainties of 2% and 2.8% respectively. Using this standard, we evaluate the response of two different IGs to a variety of different gas species and report variations of up to 20% for their measured calibration factors. We also observe a non-linear response of the IG readings for CO2 gas. Finally, we demonstrate the use of a magneto-optical trap (MOT) as a transfer standard to extend the measurement range by a factor of 100 to include pressures up to P ~ 10−5 Pa.
We report the realization of the first cold-atom primary standard. This standard is based on a universal law governing quantum diffractive collisions between particles that allows an experimental determination of the velocity averaged total collision cross section, the only parameter required to quantify the pressure or flux of particles given a sensor particle collision rate measurement. Using an ensemble of 87Rb sensor atoms, we show that this new quantum pressure standard can be applied to gases of both atomic (He, Ar, and Xe) and molecular species (, , and ), surpassing the scope of existing orifice flow pressure standards. We verify the accuracy of this new standard using an ionization gauge (IG) calibrated for N2 by an orifice flow standard. The gauge calibration factors determined by the cold atom and orifice flow standards differ by less than 0.5% and, thus, agree within their uncertainties of 2% and 2.8% respectively. Using this standard, we evaluate the response of two different IGs to a variety of different gas species and report variations of up to 20% for their measured calibration factors. We also observe a non-linear response of the IG readings for CO2 gas. Finally, we demonstrate the use of a magneto-optical trap (MOT) as a transfer standard to extend the measurement range by a factor of 100 to include pressures up to P ~ 10−5 Pa.
We describe how laser-cooled and trapped alkali-metal atoms have been used as pressure sensors in the high- and ultra-high-vacuum regimes operating with relative uncertainties of just over a percent at pressures from a few nPa and up to a few tens of μμμPa. These sensors can serve as primary standards of pressure as the determination of pressure requires only knowledge of collision cross sections between atoms and molecules, eliminating the need for calibration with other devices. The collision cross sections can be measured independently or computed with rigorous quantum methods at percent relative accuracies. We argue that this technology has advanced sufficiently to provide an alternative to the existing, expensive pressure standard in the ultra-high vacuum regime, the orifice flow standard. Experiments with trapped atoms can be used to calibrate cheaper pressure sensors (such as devices based on ionization gauges). However, the technology has not yet matured enough to be of use in other research fields because of the complexity and cost of the experiments. We propose a roadmap for this new pressure standard for vacuum metrology.
Abstract The room-temperature, velocity-averaged, total cross section for atom–atom and atom–molecule collisions can be approximated using a universal function depending only on the magnitude of the leading order dispersion coefficient, C 6. This feature of the total cross section together with the universal function for the energy distribution transferred by glancing angle collisions ( p QDU6 (Booth et al 2019 New J. Phys. 21 102001)) can be used to empirically determine the total collision cross section and realize a self-calibrating, vacuum pressure standard. This was previously validated for Rb+N2 and Rb+Rb collisions. However, the post-collision energy distribution is expected to deviate from p QDU6 in the limit of small C 6 and small reduced mass. Here we observe this deviation experimentally by performing a direct cross-species loss rate comparison for Rb+H2 and Li+H2 collisions. We measure a velocity averaged total collision cross section ratio of R = ⟨ σ tot v ⟩ Li+H 2 : ⟨ σ tot v ⟩ Rb+H 2 = 0.83 ( 5 ) . Based on an ab initio computation of ⟨ σ tot v ⟩ Li+H 2 = 3.104 × 10 − 15 m3 s−1, we deduce ⟨ σ tot v ⟩ Rb+H 2 = 3.6 ( 2 ) × 10
Atoms constitute promising quantum sensors for a variety of scenarios including vacuum metrology. Key to this application is knowledge of the collision rate coefficient of the sensor atom with the particles being detected. Prior work demonstrated that, for room-temperature collisions, the total collision rate coefficient and the trap depth dependence of the sensor atom loss rate from shallow traps are both universal, independent of the interaction potential at short range. It was also shown that measurements of the energy transferred to the sensor atom by the collision can be used to estimate the total collision rate coefficient. However, discrepancies found when comparing the results of this and other methods of deducing the rate coefficient call into question its accuracy. Here the universality hypothesis is reexamined and an important correction is presented. We find that measurements of the postcollision recoil energy of sensor atoms held in shallow magnetic traps only provide information about the interaction potential at the very largest interatomic distances (e.g., the value of C6{C}_{6}C6​ for a leading order term of $\ensuremath{-}{C}_{6}/{r}^{6}$). As other non-negligible terms exist at medium and long ranges, the total collision rate coefficient, even if universal, can differ from that computed solely from the value of C6{C}_{6}C6​. By incorporating these other long-range terms into a simple semiclassical (SC) calculation, we find the SC prediction matches that of full, multichannel, quantum mechanical scattering calculations using the complete potential. This work resolves the discrepancies, demonstrates the simplicity of estimating the rate coefficients for universal collision partners, and provides guidance for using atoms as a self-calibrating primary quantum pressure standard.